Investment Analysis and Risk Assessment

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Questions and Answers

What is the formula for calculating the holding-period return (HPR)?

(Ending price - Beginning price + dividend) / Beginning price (correct)

Ending price - Beginning price / Initial investment

(Beginning price + dividend) / Ending price

Ending price - Beginning price + dividend / Ending price

If a stock is purchased for $25, sold for $27, and distributes $1.25 in dividends, what is the holding-period return (HPR)?

13.00% (correct)

12.50%

9.00%

10.00%

What is indicated by an average return over multiple time periods?

Returns are guaranteed to be positive in all scenarios.

Investors will always lose money if they invest long-term.

The average return may vary depending on investor contributions. (correct)

The total return is greater in shorter time frames.

Which of the following factors can affect the holding-period return (HPR)?

Dividends or coupon payments in addition to capital gains Signup and view all the answers

In the context of mutual funds, what is a net investment?

Cash inflow minus cash outflow from investors Signup and view all the answers

What is the relationship between the standard deviation of the complete portfolio and that of the risky asset?

The standard deviation of the complete portfolio is y times that of the risky asset. Signup and view all the answers

What happens to the risk premium of the complete portfolio when the weight on the risky asset increases from 0.5 to 1?

The risk premium increases from 4% to 8%. Signup and view all the answers

What can be inferred about the standard deviation of the risk-free asset?

The standard deviation of the risk-free asset is zero. Signup and view all the answers

How does the standard deviation of the complete portfolio change when the investment in the risky asset is doubled?

The standard deviation doubles from 11% to 22%. Signup and view all the answers

What is the formula for calculating the risk premium of a portfolio?

Risk Premium = $E(r_p) - r_f$ Signup and view all the answers

How does the risk premium on a risky asset relate to an investor's risk aversion?

It increases with higher risk aversion. Signup and view all the answers

What does the Sharpe Ratio represent?

The ratio of portfolio risk premium to standard deviation. Signup and view all the answers

In the context of portfolio management, what does 'y' represent?

The weight allocated to the risky asset. Signup and view all the answers

Which of the following statements about T-bills as a risk-free asset is true?

They offer a return of $r_f$ with a standard deviation of 0. Signup and view all the answers

If the excess return of the complete portfolio is calculated as y times that of the risky asset, what does 'y' reflect?

The proportion of investment in the risky asset. Signup and view all the answers

Which of the following describes the relationship between the expected return and risk for a portfolio involving both risky and risk-free assets?

The expected return increases with a higher weight on the risky asset. Signup and view all the answers

What is the expected return of the levered complete portfolio if it includes a 50% investment in a risky portfolio with an expected return of 15%?

17.4% Signup and view all the answers

Which effect does borrowing at a rate higher than the risk-free rate have on the Capital Allocation Line (CAL)?

It results in a lower expected return on the complete portfolio. Signup and view all the answers

What happens to the Sharpe ratio when an investor borrows at a higher rate than the risk-free rate?

It decreases due to higher costs. Signup and view all the answers

Which of the following represents a situation where an investor's risk aversion is low?

Holding a large proportion of risky assets. Signup and view all the answers

If an investor's complete portfolio's expected return is $17.4 ext{%}$, what can be inferred about their risk profile?

They are likely leveraging their investments. Signup and view all the answers

What is the standard deviation of the complete portfolio when weights of -0.4 in the risk-free asset and 1.4 in the risky portfolio are employed?

30.8% Signup and view all the answers

How is the Sharpe ratio defined?

The difference between expected return and risk-free rate divided by the uncertainty of the portfolio. Signup and view all the answers

What is a characteristic of the Capital Allocation Line (CAL) when borrowing occurs at the risk-free rate?

It will have a constant slope. Signup and view all the answers

What defines the Capital Market Line (CML)?

The relationship between risk and return for all possible risky portfolios. Signup and view all the answers

How is the reward-to-variability ratio (Sharpe ratio) calculated?

By subtracting the risk-free rate from the expected return and then dividing by the standard deviation. Signup and view all the answers

What happens when an investor chooses a passive investment strategy?

The investor holds a market index portfolio to replicate the index returns. Signup and view all the answers

What is the expected rate of return when an investor invests proportion y in a risky portfolio?

It is a weighted average of the risk-free rate and the risky portfolio's expected return. Signup and view all the answers

If a client invests $7,000 in a risky portfolio and $3,000 in a T-bill, what is the total investment?

$10,000 Signup and view all the answers

What is the standard deviation of the client's overall portfolio if the proportion of investment y is 0.7 and the standard deviation of the risky portfolio is 27%?

18.9% Signup and view all the answers

When the expected return of a client's overall portfolio is 15%, what proportion y of his budget was invested in the risky portfolio?

0.8 Signup and view all the answers

What does a higher Sharpe ratio indicate about a portfolio?

It provides a better risk-adjusted return. Signup and view all the answers

Study Notes

Average Return over Multiple Time Periods

Holding-period return (HPR): Represents the total return received from holding an asset over a certain period. It is calculated by dividing the capital gain plus dividends or coupons by the initial investment.
HPR is the sum of capital gain yield and dividend yield: This is the basic formula for calculating HPR.
Example of calculating HPR: A stock bought for 25,soldfor25, sold for 25,soldfor27, and distributed $1.25 in dividends would have a HPR of 13%.

Scenario Analysis

Scenario analysis is a method for assessing risk. It involves creating different possible future scenarios and estimating the returns for each scenario.
The analysis helps to understand the range of possible outcomes and the likelihood of each outcome. Important in risk management.

Risk Aversion and Risk Premium

Risk aversion is the degree to which investors dislike risk.
Risk premium is the additional expected return an investor requires to compensate for taking on risk.
The size of the risk premium depends on the investor's risk aversion and the riskiness of the portfolio return. This relationship is crucial for understanding how different investors will allocate their portfolios.

Asset Allocation Problem with One Risk-Free Asset and One Risky Asset

The asset allocation problem involves deciding how to split investments between safe and risky assets.
The most basic version involves a risk-free asset (e.g. Treasury Bills) and a risky asset (e.g. a single stock or a stock portfolio). The goal is to find the optimal balance for the investor based on their risk tolerance.
Complete portfolio's expected return and standard deviation are influenced by the weight on the risky asset. The weight (y) determines the proportion of the risk-free asset and the risky asset in the portfolio.

Capital Allocation Line (CAL)

CAL represents the set of portfolios that can be created by combining a risk-free asset and a risky asset.
The slope of CAL is the Sharpe ratio, which measures risk-adjusted return (reward-to-volatility). Optimal asset allocation depends on the investor's risk aversion.
The CAL can be modified if the investor borrows at a higher interest rate than the risk-free rate. This would cause the line to become kinked with a flatter slope on the leveraged portion, impacting the Sharpe ratio and potentially altering the optimal investment strategy.

Capital Market Line (CML)

CML is a special CAL that uses a market portfolio instead of a single risky asset.
It represents the investment opportunity of the risky portfolio for a passive investment strategy, like indexing.
The CML helps investors understand the relationship between risk and return for market-related investments.

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Description

Explore key concepts in investment analysis including Holding-Period Return, scenario analysis, and the principles of risk aversion and risk premium. This quiz test your understanding of how returns and risks interact in the financial market. Perfect for finance students and professionals.